Noncooperative Formation of Coalitions in

We study a bargaining procedure of coalition formation in the class of hedonic games, where playerspreferences depend solely on the coalition they belong to. We show that if a hedonic game is to-tally balanced then for every core element there exists a stationary perfect equilibrium that supports it. The reverse is not true and it is established by means of a counter example. We also identify a condi-tion that guarantees both uniqueness of the core as well of stationary perfect equilibria. In the other extreme, we identify a condition that guarantees the emptiness of the core as well as the non-existence of stationary perfect equilibria in the roommate problem. Moreover, we show that if the game has an empty core then the stationary perfect equilibrium, if it exists, will involve unacceptable o¤ers